Question 1

A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?

Accepted Answer

No. As motion is a change in position of an object with respect to time or a reference point, it is not an example of periodic motion.

Question 2

A particle executing simple harmonic motion comes to rest at the extreme positions. Is the resultant force on the particle zero at these positions according to Newton's first law?

Accepted Answer

No. The resultant force on the particle is maximum at the extreme positions.

Question 3

Can simple harmonic motion take place in a non-inertial frame? If yes, should the ratio of the force applied with the displacement be constant?

Accepted Answer

Yes. Simple harmonic motion can take place in a non-inertial frame. However, the ratio of the force applied to the displacement cannot be constant because a non-inertial frame has some acceleration with respect to the inertial frame. Therefore, a fictitious force should be added to explain the motion.

Question 4

A particle executes simple harmonic motion. If you are told that its velocity at this instant is zero, can you say what is its displacement? If you are told that its velocity at this instant is maximum, can you say what is its displacement?

Accepted Answer

No, we cannot say anything from the given information. To determine the displacement of the particle using its velocity at any instant, its mean position has to be known.

Question 5

A small creature moves with constant speed in a vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a sample harmonic motion?

Accepted Answer

Yes, its shadow on a horizontal plane moves in simple harmonic motion. The projection of a uniform circular motion executes simple harmonic motion along its diameter (which is the shadow on the horizontal plane), with the mean position lying at the centre of the circle.

Question 6

A particle executes simple harmonic motion Let P be a point near the mean position and Q be a point near an extreme. The speed of the particle at P is larger than the speed at Q. Still the particle crosses Pand Q equal number of times in a given time interval. Does it make you unhappy?

Accepted Answer

No. It does not make me unhappy because the number of times a particle crosses the mean and extreme positions does not depend on the speed of the particle.

Question 7

In measuring time period of a pendulum, it is advised to measure the time between consecutive passage through the mean position in the same direction. This is said to result in better accuracy than measuring time between consecutive passage through an extreme position. Explain.

Accepted Answer

The mean position of a particle executing simple harmonic motion is fixed, whereas its extreme position keeps on changing. Therefore, when we use stop watch to measure the time between consecutive passage, we are certain about the mean position.

Question 8

It is proposed to move a particle in simple harmonic motion on a rough horizontal surface by applying an external force along the line of motion. Sketch the graph of the applied force against the position of the particle. Note that the applied force has two values for a given position depending on whether the particle is moving in positive or negative direction.

Accepted Answer

Figure (a) shows the graph of the applied force against the position of the particle.

Question 9

Can the potential energy in a simple harmonic motion be negative? Will it be so if we choose zero potential energy at some point other than the mean position?

Accepted Answer

No. It cannot be negative because the minimum potential energy of a particle executing simple harmonic motion at mean position is zero. The potential energy increases in positive direction at the extreme position.

Question 10

The energy of system in simple harmonic motion is given by E=21​mω2A2. Which of the following two statements is more appropriate?(A) The energy is increased because the amplitude is increased.(B) The amplitude is increased because the energy is increased.

Accepted Answer

Statement A is more appropriate because the energy of a system in simple harmonic motion is given by E=21​mω2A2.If the mass (m) and angular frequency (ω) are made constant, Energy (E) becomes proportional to the square of amplitude (A2 ).i.e. E ∝ A2 Therefore, according to the relation, energy increases as the amplitude increases.

Question 11

A pendulum clock gives correct time at the equator. Will it gain time or loose time as it is taken to the poles?

Accepted Answer

According to the relation : T=2πgl​​ The time period (T) of the pendulum becomes proportional to the square root of inverse of g if the length of the pendulum is kept constant.i.e. T∝g1​​   Also, acceleration due to gravity (g) at the poles is more than that at equator. Therefore, the time period decreases and the clock gains time.

Question 12

Can a pendulum clock be used in an earth-satellite?

Accepted Answer

No. According to the relation :T=2πgl​​The time period of the pendulum clock depends upon the acceleration due to gravity. As the earth-satellite is a free falling body and its geffective (effective acceleration due to gravity ) is zero at the satellite, the time period of the clock is infinite.

Question 13

A hollow sphere filled with water is used as the bob of a pendulum. Assume that the equation for simple pendulum is valid with the distance between the point of suspension and centre of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?

Accepted Answer

The time period of a pendulum depends on the length and is given by the relation , T=2πgl​​As the effective length of the pendulum first increases and then decreases, the time period first increases and then decreases.

Question 14

A block of known mass is suspended from a fixed support through a light spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?

Accepted Answer

Yes.Time period of a spring mass system is given by,T=2πkm​​  ...(1)    where m is mass of the block, and k is the spring constantTime period is also given by the relation,T=2πgx0​​​    ...(2)where, x0​  is extension of the spring, and g is acceleration due to gravityFrom the equations (1) and (2), we have:mg=kx0​⇒k=x0​mg​  Substituting the value of k in the above equation, we get:⇒k=x0​mg​Thus, we can find the time period if the value of extension x0​  is known.

Question 15

A platoon of soldiers marches on a road in steps according to the sound of a marching band. The band is stopped and the soldiers are ordered to break the steps while crossing a bridge. Why?

Accepted Answer

When the frequency of soldiers' feet movement becomes equal to the natural frequency of the bridge, and resonance occurs between soldiers' feet movement and movement of the bridge, maximum transfer of energy occurs from soldiers' feet to the bridge, which increases the amplitude of vibration. A continued increase in the amplitude of vibration, however, may lead to collapsing of the bridge.

Question 16

The force acting on a particle moving along X-axis is F = −k(x − vo​t) where k is a positive constant. An observer moving at a constant velocity vo​ along the X-axis looks at the particle. What kind of motion does he find for the particle?

Accepted Answer

As the observer moves with a constant velocity along the same axis, he sees the same force on the particle and finds the motion of the particle is not simple harmonic motion.

Question 17

A student says that he had applied a force F=−kx​ on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he was worked only with positive x and no other force acted on the particle.

Accepted Answer

As x  increases k  increases.A body is said to be in simple harmonic motion only when,F=−kx.....(1) where F  is force,k  is force constant, andx  is displacement of the body from the mean position.Given:F=−kx​ ......(2)On comparing the equations (1) and (2), it can be said that in order to execute simple harmonic motion, k  should be proportional to x​ . Thus, as x  increases k  increases.

Question 18

The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is

Accepted Answer

An extreme position One oscillation is said to be completed when the particle returns to the extreme position i.e. from where it started.

Question 19

The time period of a particle in simple harmonic motion is equal to the smallest time between the particle acquiring a particular velocity v . The value of v is

Accepted Answer

vmax​ Because the time period of a simple harmonic motion is defined as the time taken to complete one oscillation.

Question 20

The displacement of a particle in simple harmonic motion in one time period is

Accepted Answer

zeroDisplacement is defined as the distance between the starting and the end point through a straight line. In one complete oscillation, the net displacement is zero as the particle returns to its initial position.

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Solution for Class 11, Physics, Oscillations

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